A Lower and Upper Bound Method for Complex System Reliability Evaluation

It is hard for the existing methods to obtain the expression of the system reliability for most of the practical complex systems with a large number of components and possible stales. A new regression algorithm based on the lower and upper bounds is presented in this paper, which can obtain the system reliability analytically without concerning the structure of the complex system. The method has been applied to a real system and the reliability results are compared with those acquired by the classical method and the parametric method. The effectiveness and accuracy of the proposed method have been testified.

Optimization of Generator Based on Gaussian Process Regression Model with Conditional Likelihood Lower Bound Search

The noise that comes from finite element simulation often causes the model to fall into the local optimal solution and over fitting during optimization of generator.Thus,this paper proposes a Gaussian Process Regression(GPR)model based on Conditional Likelihood Lower Bound Search(CLLBS)to optimize the design of the generator,which can filter the noise in the data and search for global optimization by combining the Conditional Likelihood Lower Bound Search method.Taking the efficiency optimization of 15 kW Permanent Magnet Synchronous Motor as an example.Firstly,this method uses the elementary effect analysis to choose the sensitive variables,combining the evolutionary algorithm to design the super Latin cube sampling plan;Then the generator-converter system is simulated by establishing a co-simulation platform to obtain data.A Gaussian process regression model combing the method of the conditional likelihood lower bound search is established,which combined the chi-square test to optimize the accuracy of the model globally.Secondly,after the model reaches the accuracy,the Pareto frontier is obtained through the NSGA-II algorithm by considering the maximum output torque as a constraint.Last,the constrained optimization is transformed into an unconstrained optimizing problem by introducing maximum constrained improvement expectation(CEI)optimization method based on the re-interpolation model,which cross-validated the optimization results of the Gaussian process regression model.The above method increase the efficiency of generator by 0.76%and 0.5%respectively;And this method can be used for rapid modeling and multi-objective optimization of generator systems.

A Generalized Upper and Lower Solution Method for Singular Discrete Boundary Value Problems

This paper presents new existence results for singular discrete boundary value problems. In particular our nonlinearity may be singular in its dependent variable and is allowed to change sign.

Lower bound on BER performance for maximal ratio combining with weighting errors

The theoretical lower bounds on mean squared channel estimation errors for typical fading channels are presented by the infinite-length and non-causal Wiener filter and the exact closed-form expressions of the lower bounds for different channel Doppler spectra are derived. Based on the obtained lower bounds on mean squared channel estimation errors, the limits on bit error rate （BER） for maximal ratio combining （MRC） with Gaussian distributed weighting errors on independent and identically distributed （i. i. d） fading channels are presented. Numerical results show that the BER performances of ideal MRC are the lower bounds on the BER performances of non-ideal MRC and deteriorate as the maximum Doppler frequency increases or the SNR of channel estimate decreases.

The Estimation for Lower Bounds of the Solutions of Fermat's Equation

Let p be a prime with p≡3(mod 4). In this paper,by using some results relate the representation of integers by primitive binary quadratic forms,we prove that if x,y,z are positive integers satisfying x^p+y^p=z^p, p|xyz, x<y<z, then y>p^(6p-2)/2.

A Combination of N2 and CO2 Adsorption to Characterize Nanopore Structure of Organic-Rich Lower Silurian Shale in the Upper Yangtze Platform, South China： Implications for Shale Gas Sorption Capacity

The pores in shales are mainly of nanometer-scale, and their pore size distribution is very important for the preservation and exploitation of shale gas. This study focused on the organic-rich Lower Silurian black shale from four wells in the Upper Yangtze Platform, and their TOC, mineralogical composition and pore characterization were investigated. Low pressure N2 and CO2 adsorption were conducted at 77.35 K and 273.15 K, respectively, and the pore structures were characterized by modified Brunauer-Emmett-Teller （BET）, Dubinin-Radushkevich （DR）, t-plot, Barrett- Joyner-Halenda （BJH） and density functional theory （DFT） methods and then the relationship between pore structure and shale gas sorption capacity was discussed. The results indicate that （1） The Lower Silurian shale has high TOC content of 0.92%~96%, high quartz content of 30.6%-69.5%, and high clays content of 24.1%-51.2%. The total specific surface area varies from 7.56 m^2/g to 25.86 m^2/g. Both the total specific surface area and quartz content are positively associated with the TOC content. （2） Shale samples with higher TOC content have more micropores, which results in more complex nanopore structure. Micropore volumes/surface areas and non-micropore surface areas all increase with the increasing TOC content. （3） A combination of N2 and CO2 adsorption provides the most suitable detection range （~0.3-60 nm） and has high reliability and accuracy for nanopore structure characterization. （4） The TOC content is the key factor to control the gas sorption capacity of the Lower Silurian shale in the Upper Yangtze Platform.

LOWER BOUNDS ESTIMATE FOR THE BLOW-UP TIME OF A NONLINEAR NONLOCAL POROUS MEDIUM EQUATION

The lower bounds for the blow-up time of blow-up solutions to the nonlinear nolocal porous equation ut=△u^m＋u^p∫Ωu^qdxwith either null Dirichlet boundary condition or homogeneous Neumann boundary condi- tion is given in this article by using a differential inequality technique.

Upper Devonian and Lower Carboniferous Sequence Stratigraphy of South China

In South China four depositional sequences are recognized in the upper part of Upper Devonian and Tournaisian. They are named SQ0 SQ1, SQ2 and SQ3 in ascending order. SQ0 is Strunian (uppermost Devonian), and the other three Tournaisian in age. These four depositional sequences appear to correlate fairly well with the four sequence recognized in Europe, North America and other areas. This may suggest that these sequences are synchronous depos- its resulted from the eustatic changes. The present study on sequence stratigraphy, biostratigraphy and event stratigraphy indicates that in neritic facies areas of South China, the Devonian-Carboniferous boundary, matching the boundary between Siphonodella praesulcata zone and S. sulcata zone in pelagic facies areas, is not only higher than the top of the Cystophrentis zone, but also higher than the top of the Devonian-Carboniferous boundary event bed. In neritic facies areas, the Devonian-Carbonifrerous boundary is marked by the most distinct transgressive surface within the Cystophrentiseudouralina interval zone, i. e. at the base of the TST of the SQ1. This boundary coincides with the top surface of the event bed resulted from the eustatic fall, and approximately corresponds to the basal part of Rseudouralina assemblage zone.

Ramp facies in an intracratonic basin:A case study from the Upper Devonian and Lower Carboniferous in central Hunan,southern China

Detailed studies on Late Devonian to Early Carboniferous carbonate rocks in central Hunan, southern China have led to the recognition of 25 lithofacies which can be grouped into： （I） inner ramp peritidal platform, （2） inner ramp organic hank and mound, （3） mid ramp, （4） outer ramp, and （5） shelf basin facies associations. The peritidal platform facies association dominates the Zimenqiao Formation （Namurian A or late Datangian） and is characterized by gypsum and dolostone-containing sequences, indicating a peritidal platform environment. The other four facies associations dominate the Menggongao Formation （late Famennian）, Liujiatang Formation （Tournaisian or Yangruanian）, Shidengzi Formations （early Visean or early Datangian）. Five upward-shallowing cycles were distinguished in these three Formations. The predominant facies associations developed in each Formation demonstrate an overall transgression-regression cycle in the Late Devonian to Early Carboniferous in central Hunan. The overall transgressive sequence was preserved in the Shaodong, Menggongao, and Liujiatang Formations, and the overall regressive sequence was preserved in the Liujiatang, Shidengzi, Ceshui and Zimenqiao Formations.

Controls on the organic carbon content of the lower Cambrian black shale in the southeastern margin of Upper Yangtze

Control of various factors, including mineral components, primary productivity and redox level, on the total organic carbon(TOC) in the lower Cambrian black shale from southeastern margin of Upper Yangtze(Taozichong, Longbizui and Yanbei areas) is discussed in detail in this article. Mineral components in the study strata are dominated by quartz and clay minerals. Quartz in the Niutitang Formation is mainly of biogenic origin, and the content is in positive correlation with TOC, while the content of clay minerals is negatively correlated with TOC. Primary productivity, represented by the content of Mobio(biogenic molybdenum), Babio(biogenic barium) and phosphorus, is positively correlated with TOC. The main alkanes in studied samples are nCC, and odd–even priority values are closed to 1(0.73–1.13), which suggest the organic matter source was marine plankton. Element content ratios of U/Th and Ni/Co and compound ratio Pr/Ph indicate dysoxic–anoxic bottom water, with weak positive relative with TOC. In total, three main points can be drawn to explain the relationship between data and the factors affecting organic accumulation:(1) quartz-rich and clay-mineral-poor deep shelf–slope–basin environment was favorable for living organisms;(2) high productivity provided the material foundation for organic generation;(3) the redox conditions impact slightly on the content of organic matter under high productivity and dysoxic–anoxic condition.

Differences of Hydrocarbon Enrichment between the Upper and the Lower Structural Layers in the Tazhong Paleouplift

The Tazhong paleouplift is divided into the upper and the lower structural layers, bounded by the unconformity surface at the top of the Ordovician carbonate rock. The reservoirs in the two layers from different parts vary in number, type and reserves, but the mechanism was rarely researched before. Therefore, an explanation of the mechanism will promote petroleum exploration in Tazhong paleouplift. After studying the evolution and reservoir distribution of the Tazhong paleouplift, it is concluded that the evolution in late Caledonian, late Hercynian and Himalayan periods resulted in the upper and the lower structural layers. It is also defined that in the upper structural layer, structural and stratigraphic overlap reservoirs are developed at the top and the upper part of the paleouplift, which are dominated by oil reservoirs, while for the lower structural layer, lithological reservoirs are developed in the lower part of the paleouplift, which are dominated by gas reservoirs, and more reserves are discovered in the lower structural layer than the upper. Through a comparative analysis of accumulation conditions of the upper and the lower structural layers, the mechanism of enrichment differences is clearly explained. The reservoir and seal conditions of the lower structural layer are better than those of the upper layer, which is the reason why more reservoirs have been found in the former. The differences in the carrier system types, trap types and charging periods between the upper and the lower structural layers lead to differences in the reservoir types and distribution. An accumulation model is established for the Tazhong paleouplift. For the upper structural layer, the structural reservoirs and the stratigraphic overlap reservoirs are formed at the upper part of the paleouplift, while for the lower structural layer, the weathering crust reservoirs are formed at the top, the reef-flat reservoirs are formed on the lateral margin, the karst and inside reservoirs are formed in the lower part of the paleouplift.

Upper bound solution for supporting pressure acting on shallow tunnel based on modified tangential technique

Based on the nonlinear failure criterion and the upper bound theorem, the modified tangential technique method was proposed to derive the expression of supporting pressure acting on shallow tunnel. Instead of the same stress state, different normal stresses on element boundaries were used. In order to investigate the influence of different factors on supporting pressures, the failure mechanism was established. The solution of supporting pressure, with different parameters, was obtained by optimization theory. The corresponding failure mechanism and numerical results were presented. In comparison with the results using the single tangential technique method, it is found that the proposed method is effective, and the good agreement shows that the present solution of supporting pressure is reliable.

Pseudo-static analysis of cantilever retaining walls using upper bound limit analysis approach

Given the extensive utilization of cantilever retaining walls in construction and development projects,their optimal design and analysis with proper attention to seismic loads is a typical engineering problem.This research presents a new algorithm for pseudo-static analysis of retaining walls employing upper bound method.The algorithm can be utilized to design and check the external and internal stability of the wall based on the proposed mechanism.One of the main features of this algorithm is its ability to determine the critical condition of failure wedges,the minimum safety factor and maximum force acting on the wall,as well as the minimum weight of the wall,simultaneously,by effectively using the multi-objective optimization.The results obtained by the proposed failure mechanisms show that,while using the upper bound limit analysis approach,the active force should be maximized concurrent with optimizing the direction of the plane passing through the back of the heel.The present study also applies the proposed algorithm to determine the critical direction of the earthquake acceleration coefficient.The critical direction of earthquake acceleration coefficient is defined as the direction that maximizes the active force exerted on the wall and minimizes the safety factor for wall stability.The results obtained in this study are in good agreement with those of similar studies carried out based on the limit equilibrium method and finite element analysis.The critical failure mechanisms were determined via optimization with genetic algorithm.

ON THE LOWER BOUND FOR A CLASS OF HARMONIC FUNCTIONS IN THE HALF SPACE

The main objective is to derive a lower bound from an upper one for harmonic functions in the half space, which extends a result of B. Y. Levin from dimension 2 to dimension n 〉 2. To this end, we first generalize the Carleman＇s formula for harmonic functions in the half plane to higher dimensional half space, and then establish a Nevanlinna＇s representation for harmonic functions in the half sphere by using HSrmander＇s theorem.

NEW LOWER BOUNDS FOR LEE DISCREPANCY ON TWO AND THREE MIXED LEVELS FACTORIALS

The objective of this paper is to study the issue of uniformity on asymmetrical designs with two and three mixed levels in terms of Lee discrepancy. Based on the known formulation, we present a new lower bound of Lee discrepancy of fractional factorial designs with two and three mixed levels. Our new lower bound is sharper and more valid than other existing lower bounds in literature, which is a useful complement to the lower bound theory of discrepancies.

The Impact of Cut-off Lows on Ozone in the Upper Troposphere and Lower Stratosphere over Changchun from Ozonesonde Observations

In situ measurements of the vertical structure of ozone were made in Changchun （43.53°N, 125.13°E）, China, by the Institute of Atmosphere Physics, in the summers of 2010-13. Analysis of the 89 validated ozone profiles shows the vari- ation of ozone concentration in the upper troposphere and lower stratosphere （UTLS） caused by cut-off lows （COLs） over Changchun. During the COL events, an increase of the ozone concentration and a lower height of the tropopause are observed. Backward simulations with a trajectory model show that the ozone-rich airmass brought by the COL is from Siberia. A case study proves that stratosphere-troposphere exchange （STE） occurs in the COL. The ozone-rich air mass transported from the stratosphere to the troposphere first becomes unstable, then loses its high ozone concentration. This process usually happens during the decay stage of COLs. In order to understand the influence of COLs on the ozone in the UTLS, statistical analysis of the ozone profiles within COLs, and other profiles, are employed. The results indicate that the ozone concentrations of the in-COL profiles are significantly higher than those of the other profiles between ±4 km around the tropopause. The COLs induce an increase in UTLS column ozone by 32% on average. Meanwhile, the COLs depress the lapse-rate tropopause （LRT）/dynamical tropopause height by 1.4/1.7 km and cause the atmosphere above the tropopause to be less stable. The influence of COLs is durable because the increased ozone concentration lasts at least one day after the COL has passed over Changchun. Furthermore, the relative coefficient between LRT height and lower stratosphere （LS） column ozone is -0.62, which implies a positive correlation between COL strength and LS ozone concentration.

Upper bound solutions of stability factor of shallow tunnels in saturated soil based on strength reduction technique

Based on the upper bound theorem of limit analysis,the factor of safety for shallow tunnel in saturated soil is calculated in conjunction with the strength reduction technique.To analyze the influence of the pore pressure on the factor of safety for shallow tunnel,the power of pore pressure is regarded as a power of external force in the energy calculation.Using the rigid multiple-block failure mechanism,the objective function for the factor of safety is constructed and the optimal solutions are derived by employing the sequential quadratic programming.According to the results of optimization calculation,the factor of safety of shallow tunnel for different pore pressure coefficients and variational groundwater tables are obtained.The parameter analysis shows that the pore pressure coefficient and the location of the groundwater table have significant influence on the factor of safety for shallow tunnel.

Upper bound analytical solution for surrounding rock pressure of shallow unsymmetrical loading tunnels

By combining the results of laboratory model tests with relevant flow rules, the failure mode of shallow unsymmetrical loading tunnels and the corresponding velocity field were established. According to the principle of virtual power, the upper bound solution for surrounding rock pressure of shallow unsymmetrical loading tunnel was derived and verified by an example. The results indicate that the calculated results of the derived upper bound method for surrounding rock pressure of shallow unsymmetrical loading tunnels are relatively close to those of the existing "code method" and test results, which means that the proposed method is feasible. The current code method underestimates the unsymmetrical loading feature of surrounding rock pressure of shallow unsymmetrical loading tunnels, so it is unsafe; when the burial depth is less or greater than two times of the tunnel span and the unsymmetrical loading angle is less than 45°, the upper bound method or the average value of the results calculated by the upper bound method and code method respectively, is comparatively reasonable. When the burial depth is greater than two times of the tunnel span and the unsymmetrical loading angle is greater than 45°, the code method is more suitable.

UPPER-BOUND APPROACH ANALYSIS OF DRIVING POWER OF WHEEL FOR CASTEX

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LOWER BOUNDS OF BLOW UP TIME FOR A SYSTEM OF SEMI-LINEAR HYPERBOLIC PETROVSKY EQUATIONS

Li et al. in [3] obtained blow-up results for a system of Petrovskey equations in some different cases. In this article we obtain lower bounds for the blow up time under some considerations on initial data.